For Grandmother to Granddaughter tests, X-chromosome testing is your least expensive option while obtaining very high accuracy (99.9%+).
Think about the father of the child (the son of the Grandfather), if
this man is NOT the biological father of his son, then you need know if there is any possibility that the true biological father was not a close relative. (ie, could other possible father be a brother, cousin or other type of close relative to the alledged father?)

If the answer is no, then a X-chromosome test is a great option.
All men have one X chromosome, it is passed down from Father to Daughter, woman have two X-chromosomes.
Therefore a Grandmother, her son, and her 3 Granddaughters will all have at least one of their X-chromosomes exactly the same.

X-chromosome:
The X chromosome, found in both males and females, is more than 153 million base pairs and contains roughly 1000 genes.
Females have two X chromosomes while males have just one.

The use of X chromosomes to study genealogical relationships is still
relatively new.
The X chromosome, just like the Y, contains STRs, called
X-STRs.
The problem with studying X-STRs is that the entire X chromosome
undergoes recombination during meiosis.
In other words, in females the two X chromosomes randomly swap information and genes.
Family Tree DNA, one of the leaders of X-STR research (using methods developed by DNA-Fingerprint), uses "haplotype blocks", or regions of X-STRs that are inherited intact over several generations.

A male's X chromosome is inherited from his mother and is a mixture
of her two X chromosomes, one from her mother and one from her father.
It is therefore a mixture of the maternal grandparent's X
chromosomes.

A female inherits one X chromosome from each of her two parents. The X chromosome from her father is passed on from his mother is a mixture of her parent's (the paternal great-grandparent's) DNA, while the X chromosome from the female's mother is a mixture of her parent's (the maternal grandparent's) DNA.